This review aims to offer a pedagogical introduction to the analytic conformal bootstrap
program via a journey through selected topics. We review analytic methods which include …

We review the holographic correspondence between field theories and string/M theory,
focusing on the relation between compactifications of string/M theory on Anti-de Sitter …

A bstract We study the fundamentals of quantum field theory on a rigid de Sitter space. We
show that the perturbative expansion of late-time correlation functions to all orders can be …

We explore the Mellin representation of conformal correlation functions recently proposed by
Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes …

We study, using the dual AdS description, the vacua of field theories where some of the
gauge symmetry is broken by expectation values of scalar fields. In such vacua, operators …

A bstract We give a detailed account of the methods introduced in [1] to calculate
holographic four-point correlators in IIB supergravity on AdS 5× S 5. Our approach relies …

A bstract We develop a new method for decomposing Witten diagrams into conformal
blocks. The steps involved are elementary, requiring no explicit integration, and operate …

Various aspects of the four point function for scalar fields in conformally invariant theories
are analysed. This depends on an arbitrary function of two conformal invariants u, v. A …

We revisit the calculation of holographic correlation functions in type-IIB supergravity on AdS
5× S 5. Results for four-point functions simplify drastically when expressed in Mellin space …

A bstract We propose and demonstrate a new use for conformal field theory (CFT) crossing
equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non …